Thursday, July 03, 2014

An Argument for the Existence of God: Step 1

By Thomas Cothran

This is the third post in the ongoing series presenting an argument for the existence of God. In this post we move into the argument itself, taking the first step toward an argument for the existence of God.

In this first step, I will show that at least one unconditioned reality exists. First, we will define what it means to be a conditioned or unconditioned reality. Then we will proceed to demonstrate that the assertion "there is no unconditioned reality" logically entails that there are no realities at all. In other words, the claim that there are no unconditioned realities is logically equivalent to saying that nothing exists.

Definitions: Realities Conditioned and Unconditioned

Our terms are drawn from Robert Spitzer's New Proofs for the Existence of God.

1.1 A conditioned reality is any reality whose existence depends in any way on some other reality. "Reality" is used very broadly here. It means not only material objects, but also physical laws, space, time--in short, anything that can be described as really existing.

1.2 An unconditioned reality is a reality whose existence does not depend on another reality for it to exist or happen. Its independence is absolute: if a reality depends upon another reality in any respect, it is conditioned.

1.3 A condition refers to any reality upon which a conditioned reality depends for its existence. A conditioned reality can have many conditions: an apple, for example, depends for its existence upon atomic and sub-atomic reality. The strong force, for example, is a condition for a given apple, for without the strong force, there would not be this apple.

The Argument

We know that at least some things are conditioned. For example, the existence of human beings depends at present upon the earth's atmosphere. Without the atmosphere, we would not be. Were it not for atomic reality, we could not exist at all. So we can say the following:

1.4 There exist some conditioned realities.

Given that we know there are at least some conditioned realities, the question is whether there is an unconditioned reality (or realities). At this point, then, there are two options: either all realities are conditioned, or of all realities, one or more is unconditioned. We can put the two options this way:

1.5 Either only conditioned realities exist, or at least one existing reality is unconditioned.

To make things simple, we can refer to the first half of 1.5, which says that only conditioned realities exist, as ~UCR (for there are no unconditioned realities), and the second half as UCR. 1.5 can be reformulated as:

1.5a Either ~UCR or UCR.

If one option is false, the other must be true. If it is either the case that A or B is true, and it is that B is not true, then A must be true. Put in logical notation, the proof looks like this:

A v B
~A
B

This form of indirect proof will be used here. I will demonstrate that the claim that only conditioned realities exist entails that no realities exist. Since this contradicts a fact we know to be true, (namely 1.4, that some conditioned realities exist), we can conclude that "only conditioned realities exist" is false. Thus, there must be at least one unconditioned reality.

Finite Regress of Conditions

Let's consider a particular conditioned reality with a finite set of conditions, and call it CR1. Any condition with a finite number of conditions will have one or more "terminal conditions." For example, CR1 has as its condition CR2, which has as its condition CR3.

If CR3 is the terminal condition, two things follow. First, CR3 does not exist, because its condition for existing is unfulfilled. (via 1.1 & 1.3) CR3 is a conditioned reality, which means that must have a further condition, CR4, that also must exist (via 1.3). But in this scenario, CR3 is the terminal condition. (The case of circular conditions, e.g., CR3 having as a condition CR1, is dealt with below.)

Second, the realities prior to CR3 in the series do not exist, because their conditions have not been fulfilled. If CR3 does not exist and CR3 is a condition for CR2, CR2 does not exist. CR2 is a condition for CR1, and therefore CR1 does not exist. (Again, we will consider the case of circular conditions below.)

Thus, we can conclude:

1.6 Any conditioned reality which has as its conditions a finite number of conditioned realities does not exist.

Consider the following table, which illustrates a simple case of CR1 having two further conditions:

Stage
1

Stage
2

Stage
3

Conditioned
reality in question

CR1

CR2

CR3

Conditions
that must be fulfilled for Conditioned Reality to Exist

CR2
exists & CR2's conditions are fulfilled

CR3
exists & CR2's conditions are fulfilled

CR4
exists & CR4's conditions are fulfilled

Present
CR's existential conditions met?

No

No.

No

Previous
CR's existential conditions met?

No

No

No

Compare to the following table, in which CR1's condition, CR2, is conditioned by an unconditioned reality:

Stage
1

Stage
2

Stage
3

Conditioned
reality in question

CR1

CR2

UCR3

Conditions
that must be fulfilled for Conditioned Reality to Exist

CR2
exists & CR2's conditions are fulfilled

CR3
exists & CR2's conditions are fulfilled

No
conditions

Present
CR's existential conditions met?

No

No.

Yes

Previous
CR's existential conditions met?

No

No

Yes

Infinite Regress of Conditions

What about a conditioned reality with an infinite number of conditions that are likewise conditioned realities? Robert Spitzer points out that this too fails:

“CR1 would have to depend on some other conditioned reality, say, CR2, in order to exist. Hence it is nothing until CR2 exists and fulfills its [CR2’s] conditions. Similarly, CR2 would also have to depend on some other conditioned reality, say CR3, for its existence, and it would likewise be nothing until CR3 exists and fulfills its conditions.”

We saw in the foregoing paragraphs that if the chain comes to a stopping point at, say CR3, anything earlier in the series cannot exist.

If the chain does not come to a stopping point, the whole series will likewise not exist. If we continue through CR4 to CR5 and onward, at no point is any condition satisfied. CR4 does not exist until CR5 exists and CR5’s condition is fulfilled; CR5 does not exist until CR6 exists and its condition for existence likewise is satisfied. At no point, no matter how far we go, can any condition be fulfilled.

The infinite regress can only pile up unfulfilled conditions, because every step introduces a new unfulfilled condition. (This is the case whether we consider the series, so to speak, ordinally or cardinally.) Every attempt to posit a conditioned reality necessarily involves co-positing a conditioned reality whose conditions is, at that step, unfulfilled.

An infinite number of conditioned conditions, then, logically entails the nonexistence of any given conditioned reality.

Thus, we can conclude:

1.7 Any conditioned reality which has as its conditions an infinite number of conditioned realities does not exist.

Stage
1

Stage
2

Stage
3

Stage
4

Conditioned
reality in question

CR1

CR2

CR3

CR4

Conditions
that must be fulfilled for Conditioned Reality to Exist

CR2
exists & CR2's conditions are fulfilled

CR3
exists & CR2's conditions are fulfilled

CR4
exists & CR4's conditions are fulfilled

CR5
exists & CR5's conditions are fulfilled....

Present
CR's existential conditions met?

No

No.

No

No...

Previous
CR's existential conditions met?

No

No

No

No...

As the illustration shows, at no stage of an infinite regress will any condition be satisfied.

Circular Conditions

But what if we posit a circular series of conditioned conditions for CR1? What if we say that CR1 has the condition CR2, which in turn has the condition CR3, which finally has the condition CR1? This can be quickly disposed of. Just as with an infinite chain, at no point, no matter how many times one goes around the circle, will any condition be satisfied.

If the circular regress stops at a certain point such that one of the conditioned realities is the first condition, the argument concerning a finite set of conditions applies. If the circular regress does not stops, but circles indefinitely, the argument concerning an infinite regress applies. In either case, the logical consequence of a circular series of conditioned realities is non-existence.

This gives us the following:

1.8 - A circular series of conditions is either a finite or an infinite set of conditions.

Putting It All Together

Let's put all this together. It is either the case that there exist only conditioned realities or there exists at least one conditioned reality. (1.5) (This was also stated as either ~UCR or UCR. (1.5a))

Assume ~UCR. Let us also assume that there exists at least one thing. From these two assumptions, it follows there is at least one conditioned reality. We'll call it CR1.

CR1 must have at least one existing condition for CR1 to exist. (1.1) Any condition CR1 has must also be a conditioned reality, because we have assumed that there exist no unconditioned realities. Either CR1 has as its condition a finite or an infinite number of conditions.

Assume CR1 does not have an infinite number of conditions. (Remember that these conditions are themselves conditioned realities, because we have assumed ~UCR.) CR1 would then have a finite number of conditions. It follows from this that CR1 does not exist. (1.6)

Assume CR1 does not have a finite number of conditions. (Remember that these conditions are themselves conditioned realities, because we have assumed ~UCR.) Then CR1 would have an infinite number of conditions. It follows that CR1 does not exist. (1.7)

Therefore, if we assume that only conditioned realities exist (~UCR), CR1 does not exist. Thus, the assumption that there are only conditioned realities entail the non-existence of any conditioned realities. In addition, the assumption that only conditioned realities exist, means that no unconditioned realities exist. But any reality will either be conditioned or not.

Therefore, if the assumption that only conditioned realities exist (~UCR) entails the non-existence of anything at all. The assumption that there are only conditioned realities is logically equivalent to the assumption there are no unconditioned realities. So we can set up another sub-step:

1.9 If there are no unconditioned realities, nothing exists.

Thus, if anything exists--anything at all--there is at least one unconditioned reality. An unconditioned reality is more certain than the existence of the Atlantic Ocean, or the Peony Star, or the Milky Way galaxy. I could, after all, be a brain in a vat, with all my perceptions pumped in by a computer simulation. But in this case, the computer simulation would still exist. That is, there would be at least one existing reality. And from this it follows there is an unconditioned reality.

No matter what fantastic scenario we come up with--where we might be deceived by a demon, be a part of a computer simulation, be a brain in a vat, or so on--it is indubitably the case that something exists. Something must exist to cause these sorts of deceptions. Therefore, we can conclude that

1.10 At least one reality exists.

If it is the case that at least one reality exists, it is not the case that nothing exists. So from 1.9 and 1.10, we can deduce our conclusion:

1.10 There exists at least one unconditioned reality.

Preview of the Next Steps

This is but the first step of the argument, and it does not, of itself, demonstrate the existence of a Christian God. However, it is a very big step in that direction. There are not many candidates for an "unconditioned reality" that lack the coloring of divinity. Any physical reality cannot be unconditioned, for it depends on things like matter, its constituent parts, space, or time.

Starting down this path takes us into the next steps in the proof. The argument of Step 2 is that an unconditioned reality must be absolutely simple. The argument of step 3 will be that an unconditioned reality must be simple in all perfections. In step 4, it will be shown that an unconditioned reality must be unique--there is only one unconditioned reality. In the final step, step 5, it will be demonstrated that an unconditional reality must be the continuous creator of every conditioned reality.

I should have put a proviso in there. The causal sequences aren't necessarily temporal.

For example, one's father is generally not a condition for oneself. One's father can die, after all, but his progeny doesn't fall out of existence.

There's no assumption whatsoever about temporal sequence built into the argument. In fact, "logical" causal chains (e.g., the apple depending on the existence of atoms, atoms depending on the existence of the strong force) are much more clearly conditional sequences than temporal causal sequences are.

The argument does not say that there aren't temporally infinite causal chains; it's actually quite compatible with an eternal universe. The argument just says that an infinite sequence of conditioned realities conditioning one another won't work in the absence an unconditioned reality.

If you want to expand on your objection, I may do a separate post specifically on any objections raised.

What about a conditioned reality with an infinite number of conditions that are likewise conditioned realities? Robert Spitzer points out that this too fails:“CR1 would have to depend on some other conditioned reality, say, CR2, in order to exist. Hence it is nothing until CR2 exists and fulfills its [CR2’s] conditions. Similarly, CR2 would also have to depend on some other conditioned reality, say CR3, for its existence, and it would likewise be nothing until CR3 exists and fulfills its conditions.”

….

If the chain does not come to a stopping point, the whole series will likewise not exist. If we continue through CR4 to CR5 and onward, at no point is any condition satisfied. CR4 does not exist until CR5 exists and CR5’s condition is fulfilled; CR5 does not exist until CR6 exists and its condition for existence likewise is satisfied. At no point, no matter how far we go, can any condition be fulfilled.

Consider the parallels between Spitzer’s infinite chain of conditioned realities and the infinite chain of dichotomies in one of the manifestations of Zeno’s paradox (copied from http://plato.stanford.edu/entries/paradox-zeno/#Dic because I’m too lazy to type my own version):

”Suppose a very fast runner—such as mythical Atalanta—needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says. There's no problem there; supposing a constant motion it will take her 1/2 the time to run half-way there and 1/2 the time to run the rest of the way. Now she must also run half-way to the half-way point—i.e., a 1/4 of the total distance—before she reaches the half-way point, but again she is left with a finite number of finite lengths to run, and plenty of time to do it. And before she reaches 1/4 of the way she must reach 1/2 of 1/4 = 1/8 of the way; and before that a 1/16; and so on. There is no problem at any finite point in this series, but what if the halving is carried out infinitely many times? The resulting series contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. However it does contain a final distance, namely 1/2 of the way; and a penultimate distance, 1/4 of the way; and a third to last distance, 1/8 of the way; and so on. Thus the series of distances that Atalanta is required to run is: …, then 1/16 of the way, then 1/8 of the way, then 1/4 of the way, and finally 1/2 of the way (of course we are not suggesting that she stops at the end of each segment and then starts running at the beginning of the next—we are thinking of her continuous run being composed of such parts). And now there is a problem, for this description of her run has her travelling an infinite number of finite distances, which, Zeno would have us conclude, must take an infinite time, which is to say it is never completed. And since the argument does not depend on the distance or who or what the mover is, it follows that no finite distance can ever be traveled, which is to say that all motion is impossible.”

Spitzer is drawing upon a core commonality in the many manifestations of Zeno’s paradoxes – the supposed impossibility of traversing an infinite series of steps to a particular physical end.

One more thing, Thomas - I believe you are wrong when you claim that Spitzer's argument works against an eternally-existing infinite series of CRs. He is clearly implying that one CR must exist before another can come into being. If there are infinite CRs, and if all CRs are all eternal in their existence, then I believe Spitzer's argument falls apart.

Zeno's paradoxes conclude that change is an illusion, and that there is, in reality, only one being, which is, in our terms, unconditioned. That is to say, Zeno's argument entails that there are no conditioned realities (i.e., that contingent things have no being).

But premise 1.4 states that "there exist some conditioned realities." So not only is Zeno's argument and Spitzer's different, they contradict each other! It's like summing up Jerry Coyne's "Why Evolution is True" by saying "Lamarkism, therefore neo-Darwinism." Not only is that not the argument, but you've confused the argument with something it explicitly rejects!

There are a lot of other differences. Zeno's paradoxes aren't even about the same thing as Spitzer's argument. The notion of infinity isn't even the same: Zeno's paradoxes are about infinitely divisible magnitudes. The only type of infinity that shows up in Spitzer's argument is the possibility of a CR that has an infinite set of conditions. The question of whether magnitudes are infinitely divisible (which is the sort of infinity in Zeno) is as relevant to Spitzer's argument as whether there exist black swans.

It's important to note that the "before" and "after" refers to the relations of dependence. CR2 is before CR1 if CR1's existence depends on CR2's existence.

Not a single premise of the argument says that a condition must precede what it conditions in time. They could be simultaneous, or they could have always been. What matters is simply whether they depend on each other.

That's what's interesting about this argument. It's common for us to assume that if A is the effect of B, A precedes B in time. Thomists, however, view certain effects as simultaneous with causes. But the argument presented here works whatever the relation of cause and time might be.

"If there are infinite CRs, and if all CRs are all eternal in their existence, then I believe Spitzer's argument falls apart."

Premise 1.7 deals with this. What it shows is not that there aren't an infinite number of conditioned realities, even eternal ones, just that if there are, there must be an unconditioned reality. That's why I included the chart as an illustration. It shows visually that if you deny any unconditioned realities and posit an infinite number of conditioned realities, every conditioned reality will have an unmet condition, and will therefore not exist.

I appreciate your comments. The infinite causal series seems to be the most controversial part of the argument thus far, so I will probably do a post on it before moving on to the second step. Any further objections or comments you want to make I'll consider in that further post.